Which of the following is not a solution of `3(x-8)(x-3)(x+4)(x+7)=0`?

Options

A. `-4`
B. 0
C. 3
D. 8

Answer

To determine which of the following is not a solution of the equation \(3(x-8)(x-3)(x+4)(x+7)=0\), we need to find the values of \(x\) that make the equation equal to zero.

### Step-by-Step Solution:

1. **Set the equation to zero**:
\[ 3(x-8)(x-3)(x+4)(x+7) = 0 \]
Since the product of the terms is equal to zero, we can ignore the constant factor (3) and focus on the polynomial part.

2. **Identify the factors**:
The equation can be broken down into four factors:
- \(x - 8\)
- \(x - 3\)
- \(x + 4\)
- \(x + 7\)

3. **Set each factor to zero**:
To find the solutions, we set each factor equal to zero:
- \(x - 8 = 0 \Rightarrow x = 8\)
- \(x - 3 = 0 \Rightarrow x = 3\)
- \(x + 4 = 0 \Rightarrow x = -4\)
- \(x + 7 = 0 \Rightarrow x = -7\)

4. **List the solutions**:
The solutions to the equation are:
- \(x = 8\)
- \(x = 3\)
- \(x = -4\)
- \(x = -7\)

5. **Compare with given options**:
Now, we need to compare these solutions with the options provided in the question. The option that does not match any of the solutions we found is the one that is not a solution of the equation.

### Conclusion:
After comparing the options with the solutions \(8\), \(3\), \(-4\), and \(-7\), we can identify which option is not a solution.